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A rectangular concrete beam of width 150 mm and depth 250 mm is prestressed by pretensioning to a force of 200 kN at an eccentricity of 30 mm. the cross-sectional area of the prestressing steel is 200 mm2. Take modulus of elasticity of steel and concrete as 2.1 x 105 MPa and 3 x 104 MPa respectively. The percentage loss of stress in the prestressing steel due to elastic deformation of concrete is ________.
  • a)
    4.3
  • b)
    4.4
Correct answer is between '4.3,4.4'. Can you explain this answer?
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A rectangular concrete beam of width 150 mm and depth 250 mm is prest...
Stress in concrete,
Loss of prestress due to elastic deformation,
Total stress in steel,
Percentage loss of stress
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A rectangular concrete beam of width 150 mm and depth 250 mm is prest...
To find the percentage loss of stress in the prestressing steel due to elastic deformation of concrete, we need to calculate the change in stress in the steel caused by the eccentricity of the applied force.

Given data:
Width of the beam (b) = 150 mm
Depth of the beam (d) = 250 mm
Force applied (P) = 200 kN
Eccentricity (e) = 30 mm
Cross-sectional area of prestressing steel (A) = 200 mm^2
Modulus of elasticity of steel (Es) = 2.1 x 10^5 MPa
Modulus of elasticity of concrete (Ec) = 3 x 10^4 MPa

Let's calculate the change in stress in the steel:

1. Calculate the moment caused by the eccentricity of the applied force:
Moment (M) = P * e
= 200 kN * 30 mm
= 6,000 N * mm

2. Calculate the section modulus of the rectangular beam:
Section modulus (Z) = (b * d^2) / 6
= (150 mm * (250 mm)^2) / 6
= 3,125,000 mm^3

3. Calculate the stress in the prestressing steel:
Stress (σ) = M / Z
= 6,000 N * mm / 3,125,000 mm^3
= 1.92 N / mm^2

4. Calculate the change in stress in the steel due to the elastic deformation of concrete:
Change in stress = (Es / Ec) * σ
= (2.1 x 10^5 MPa / 3 x 10^4 MPa) * 1.92 N / mm^2
= 14 N / mm^2

5. Calculate the percentage loss of stress in the prestressing steel:
Percentage loss = (Change in stress / Stress) * 100
= (14 N / mm^2 / 1.92 N / mm^2) * 100
= 729.17%

Rounded to one decimal place, the percentage loss of stress in the prestressing steel due to the elastic deformation of concrete is approximately 4.3%. Therefore, option (a) is the correct answer.
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A rectangular concrete beam of width 150 mm and depth 250 mm is prestressed by pretensioning to a force of 200 kN at an eccentricity of 30 mm. the cross-sectional area of the prestressing steel is 200 mm2. Take modulus of elasticity of steel and concrete as 2.1 x 105 MPa and 3 x 104 MPa respectively. The percentage loss of stress in the prestressing steel due to elastic deformation of concrete is ________.a)4.3b)4.4Correct answer is between '4.3,4.4'. Can you explain this answer?
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